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ECON 2 Final: Economics 210A UCSB Final Exam 013

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turquoisegnu128
31 Jan 2019
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UCSB
Department
Economics
Course
ECON 2
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All

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There are two goods, named goods 1 and 2. Each type a has an initial endowment of 9 units of good 1 and no good 2. Each type b has an initial endowment of 16 units of good 2 and no good 1. Each type a consumer has the utility function. Let good 1 be the numeraire and let p be the price of good 2: find the excess demand function of each type of consumer for good 1. A really outstanding answer would not only nd all of the equilibria but show that there are no others. : an expected utility maximizer seeks to maximize the expected value of. She is considering whether to purchase a warranty on the product. The warranty costs c and would pay her l if the product fails. Assume that the cost of the warranty exceeds the expected loss pl from product failure.

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Related Questions

Please explain the steps to get to the answers. I already have just the answers.

Adam and Eve are consumers in a 2-consumer, 2-good exchange economy. The price of X is Px, and the price of Y is $1. Each one has an initial endowment of (X=6, Y=6); therefore, each one has a "budget line" of X*Px+ Y*Py = 6*Px + 6. Adam's utility function is U = XY. The expression for Adam's marginal rate of substitution (i.e.   ) is Y/X, which at his initial endowment of (6, 6) has the value of 1. Adam's demand for X as a function of the price of X is X = 3 + 3/PX.

If Eve's utility function is,  

find: (i) the expression for Eve's marginal rate of substitution.

(ii) the value of Eve's marginal rate of substitution at her initial endowment.

(iii) Eve's demand for X as a function of the price of X.

(iv) What is the price of X in equilibrium?

Suppose that a consumer's preferences over two goods, x and y, are represented by a Cobb-Douglas utility function:

U(x,y) = x1-i² yi²

a. Find the expenditure function of the consumer, and the compensated demand functions.

b. Suppose that i² = 1/4 and that initially a consumer is in equilibrium with px = 1,py = 1, I = 100. What are the demands for xand y.

c. What is the minimum increase in income necessary for the consumer to be as well offunder price px = 1, py = 2, as she/he was at prices px = 1, py = 1?

Explain why the percentage increase is smaller than the increase inthe CPI for the consumer that you derived in part c.

Given prices for two goods PX = 2 and PY = 3 and a budget of $120 a consumer is trying to maximize the utility function U(X, Y ) = 2X0.3Y 0.7 . Use the Lagrange method to solve this problem, but don’t worry about the second order conditions (if you wish, you can actually check that the MRS is decreasing and this utility function is well behaved). a) Write and solve the utility maximization problem subject to the budget constraint. What is the resulting value of the utility function? (U=49.0481) b) Write and solve the dual problem. Do you get the same optimal solution (the same optimal combination of X and Y)? What is the resulting expenditure? Does that match the budget of your original (primal) problem? (X=18, Y=28 should be the same as for a or very close due to rounding) c) Assume now general values for prices and income. Solve for the optimal amounts of X and Y as functions of PX, PY , and I. What conclusion can you draw regarding how you spend your budget when dealing with Cobb Douglas functions with exponents that add up to 1. You can actually try to solve the general case where we replace the exponents 0.3 and 0.7 with some α and β, where α + β = 1. (Hint: you should find that you spend percent of your income on X and β percent of your income on Y. See if you can get there by solving!)